Out of this I’ve formed Opinions about traits one should avoid, lest one look like a crank.

The easiest is the true crackpot calling card: claiming something is true that was definitively proved false long ago, such as the ability to square the circle. Typically this comes with some argument about near-sightedness, essentially, where if you just expand your viewpoint you can use techniques of the greater universe to solve all problems. Sometimes these have explicit mystical/religious tones, or allusions to historical figures who were denied but were correct. They are my favorite to read but they are the most easily dismissed.

There are three more, however, that are potential traps for legitimate scientists. Cranks will often name-drop (leading one in a respected position to be careful about replying to their questions lest it be made to look as though you are collaborators). In a standard math paper there is no need to mention anyone who is not attached to the current or cited results, except perhaps in an acknowledgement for “helpful conversation.”

Cranks will frequently feel the need to show off possession of a huge body of knowledge, even if it’s not entirely relevant. This is especially true of results that are more abstract and/or difficult, such as the Axiom of Choice. I did, however, see a legitimate paper refer to the Axiom of Choice (with an exclamation point) before admitting that it wasn’t actually necessary for the object at hand. Including it did nothing but muddy the waters.

Finally, the trait that I see with nearly every crank is urgency in claiming credit and differentiating one’s own work from that previously existing, almost to the point of defensiveness. This is easy to find in certain legitimate mathematicians’ work as well, though, if they are trying to prove themselves or otherwise have a chip on their shoulders. I read a paper where, after giving an approach that was of a similar bent, the author was quick to point out that it was similar at a high level only, and not in actual methodology.

The mathematicians I admire the most are quick to give credit and unworried about claiming it. They put in their papers only what is necessary to understand the results at hand and their context and importance, perhaps with interesting sidebars but always labeled as such. Of course, this is easier to do when you are confident of your abilities and the quality of your work, but I think emulating this appearance will help anyone come across as confident and competent. That is, decidedly not a crank.

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Textbooks and other comprehensive approaches

• Online Statistics Education, an online openly licensed statistics text with labs; outgrowth of the Rice Virtual Lab in Statistics
• StatLib, a statistics community database
• The Little Handout of Statistical Practice, online textbook

Sources for statistics

• Guide to sources of statistics from the US Census Bureau
• UNdata, international statistical data
• Facebook demographics vs. US demographics (April 2010)

Presentation of statistical information

• Graphic Sociology: evaluating visual presentation of data
• Information is Beautiful: data journalism in the form of visualization
• ChanceWiki for Chance News, reviewing news stories involving probability or statistics
• Junk Charts and Numbers Rule Your World, discussion of visual and written communication of statistical topics, respectively
• Unclear statistics explanation in a news article

Et cetera

• Why n-1 in the formula for sample standard deviation?, by Stephen A. Book
• Correlation is not causation from xkcd
• Statistics and dating from xkcd
• Stochasticity episode from Radiolab

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We went through a phase in graduate school of writing poems and songs, usually based off existing ones. I think they’re worth preserving, though I do shake my head a bit when I read some of them. I’ve given credit (blame?) below, though I did leave them in their original first-name-only state; anything not ascribed is my own handiwork.

Wonderful World
(with apologies to Sam Cooke)

Don’t know much about topology
Don’t know much Galois theory
Don’t know much about Folland’s book
Don’t know how the complex plane should look
But I do know that I love math
And I know that if it loved me back
What a wonderful world this would be.

Don’t know much about PDEs
Don’t know much about set theory
Don’t know much about Lie algebra
Don’t know what a slide rule is for
But I do know one and one is two
And if my own claims were just as true
What a wonderful world this would be.

The Wiener Covering Lemma jingle:

Oh, I wish I were a covering by Wiener
To bound the size of measurable E
With a subset that is disjoint times a constant
Depending on dimensionality!

Homotopy
(to the tune of “Oklahoma”, by Phil with help from the usual lunch crowd)

HOOOOHHHHHHHH
motopy, where the curves deform continuously
and it’s trivial
in spaces who
are called “connected simple-y”!

(incidentally, Maig and I were looking to fix the rhyme with “trivial” and the rhyming dictionary gave us “lord of misrule”, which is just really cool)

Somewhere into a Spectrum
(to the tune of “Somewhere over the Rainbow”, by Julie with my willing but not very able help. it doesn’t scan very well but it was written in a very short amount of time.)

Somewhere into a spectrum
Saunders lives
Samuel waits with omega
For your map in from X

And when the cohomology
Is found with coefficients G
It’s the same as classes, you see,
When you find homotopy.

Some explanation: Saunders and Samuel are Mac Lane and Eilenberg, respectively. If K(G,n) is an Eilenberg-Mac Lane space (the K(G,n)’s form an omega-spectrum, by the way), with G an abelian group and X a CW complex, n>0, then there is a natural bijection from the set of homotopy classes of maps X–>K(G,n) to the nth cohomology of X with coefficients in G. That is to what the song refers.

Twenty-Three Digits of Pi
(A Shakespearean rant by me and Phil)

Now I have a grand insolence
To martyr fools who prate conceits
Developed, blindly stewarded, and by our grooming,
Made subtle in measure.

The following was something I had buried in my real analysis notebook. Julie said I should share with the world because it’s funny to have such a bleak poem about something as innocuous as analysis. I’m not sure analysis is so innocuous. Anyway, this blog post is the first time it has seen the light of day.

Analytic Howl
(with groveling apology to Allen Ginsberg)

I have seen the best minds of my generation
Destroyed by madness, starving, hysterical
Driven to abstraction by the fragments of analysis
Crumbs dropped from the masters, fractions and dimensions
Sobolev wields a whip, clamoring for integration
Compute and work within epsilon for your bread.
Then Hardy, no comedian now, looms large above
The meek mathematician’s last grasp on sanity
Slips away and he weeps, tears and mucous and saliva
Mingling on the floor on which he lies.
Numerical and functional they merge
Blending together like gashes in a river
Unruly children convolve, they star, like some profanity eradicated
Regularize! the masses cry, and support the intertwining
The norm must be upheld, it keeps the rules from failing.
Signed measure takes your name and spits out
A number, a value for your life
Fubini and Tonelli weave too fast for the weeping eye to see
The integrals and functions dance a sickening
Do-si-do, shifting position, sometimes equal, sometimes less
We lose some life when we know it more.

[I should make the caveat that while I did not find analysis an easy course, I do not hold any grudge against it. I simply got going on this and I couldn’t stop. It was going to be my magnum opus until I realized I didn’t feel strongly enough about analysis to justify creating an entire rework of Howl, long, bleak, and depressing, about it.]

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Astonishingly, the links below – labeled “unchecked since 2004” – all still work as of this writing. I had them in a section headed “math entertainment.”

The Mathematical Quotation Server is perhaps not “entertainment” per se, and is definitely hard to navigate, but interesting nonetheless. I have no recollection how I came upon Math Fun with the Ramones but it is worth pointing out if only for your daily dose of dada. The most complete list of mathematician jokes I have found is this one from the Cherkaevs. A page with math humor, not all of it “jokes” strictly speaking, is the Science Jokes mathematician section. Both of the above are long single pages, but if you can wade through them there are some real gems.

In this section probably also belongs mathematical art. My favorite is Kerry Mitchell, whose work I discovered in the Phoenix Joint Meetings art display. Lo these many years later, I still have one of his pieces as my desktop wallpaper.

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